Random number generation and management method, and device

ABSTRACT

The present invention relates to a method and device for generating and managing shorter random number series, such as ID and password, in which, for the given N bits binary series R and K dimensions multi-dimensional coordinate information i (i 1 , . . . , ik, . . . , iK), R is used for the following part of the decimal point of initial value x 0  for nonlinear function, i is transformed into coordinates of each dimension, i 1 , . . . , ik, . . . , iK, and the initial value x 0  and ik are stored in the register, through operations to generate and manage multi-dimensional random number R i .

FIELD OF INVENTION

The present invention relates to a random number generation andmanagement method and device.

DESCRIPTION OF THE RELATED ART

There is not only a situation of a large number of random numbersgenerated and used in a short time during computer simulation, but alsoa situation of random numbers with finite length (such as 128 bits)generated and used in identification (ID) and password (PW). Even ID andPW require stronger security management, in fact, there is not yet adevice that achieves effective management. There are often reportsrelated to lost memory media storing user's ID and other information.

The management for the random number array of ID and PW is difficult,and currently the information is only stored in the storage of memorymedia. User's ID and other information stored in the memory media beinglost under the state without encryption shows the difficulty of themanagement.

Pseudo-random number can be regenerated. When the same random number isneeded during computer simulation, it can be generated if the initialvalue generating the random number is kept. That is, the management forthe initial value generating the random number is regarded as themanagement for the very long random number series.

On the premise of a sufficiently long periodic binary series (r₀ r₁ . .. r_(t) . . . ) (discrete-time t=0, 1, 2, . . . ), we consider thefollowing ID and PW generating and managing system. ID and PW system isgenerated and managed through an initial value by secret management andt by public management. When needed, the initial value and t are inputin the system to generate the corresponding ID or PW. But, it is clearthat it takes a long time to generate random number series (ID, PW)corresponding to a large t, and the system will lose its practicalfunction, such as t=2⁶⁴.

On the other hand, because the value series generated by the chaosfunction has special properties, such as nonlinearity, initial valuesensitivity, calculation unidirectionality, etc, it is expected to beused for random number generation. In which, some are used forgenerating random number through logistic map (Equation 1) (hereinafterreferred to as LMAP), and for inspection to the generated series(non-patent literatures 1-3).x _(t+1)=4x _(t)(1−x _(t))  Equation 1(0<x_(t)<1, t=0, 1, 2, . . . )Non-patent literature 1

Ulam, S. M. and Von Neumann, J., “On Combination of StocasticDetermistic Processes”, Bull. AMS., Vol. 53, p. 1120 (1947)

In this literature, Equation 1 is proposed to be used for generatingrandom number.

Non-patent literature 2

Tohru KOHDA and Eiji OGATA, “Bernoulli trials and Chaotic Trajectoriesin the Logistic map”, IEICE A (Japanese), Vol. J68-A No. 2 pp. 146-152(1985)

In this literature, the binary series generated through Equation 1 andthe threshold value defined as 0.5 is complete random number series.

Non-patent literature 3

K. Shono, “Chaos engineering”, Springer-Verlag Tokyo, Tokyo, 2002.

In this literature, Equation 1 applies to an effective method forhigh-speed random number generated, in which fixed decimal pointcalculation is proposed to implement hardware-based.

The calculation of chaos function LMAP has unidirectionality, that is,starting from a certain initial value x₀, x_(t) (t=1, 2, . . . ) can becalculated individually, but x₀ cannot be calculated from the calculatedx_(t). This is because if the inverse function of the second orderfunction LMAP, x_(t)=(1±√(1−x_(t+1))/2, is used for reverse calculationfor x_(t), one of the two possible states must be chosen (the choicebetween + or − symbol).

In the application, the binary series generated through the LMAP is thebinary series generated when the threshold value is 0.5 to x_(t), (ifx_(t)≧0.5, the output is 1, and if x_(t)<0.5, the output is 0).Moreover, the inventor of the application confirms that the LMAP has thefollowing features.

When the calculation accuracy is N bits, from t=0 to t=N−1, if there arecontinuously generated N bits binary series (the threshold value is0.5), the x₀ generating the binary series can be calculated through theinverse function of the LMAP. The + or − symbol is chosen on the basisof the binary value corresponding to the same t (1: +, 0: −). This isbecause the LMAP is calculated according to the divergent results of thelyapunov exponent, and the inverse function of the LMAP is calculatedaccording to the convergent results of the lyapunov exponent.

It is clear that the binary series generated by the LMAP with suchfeatures is improper to be used for the random number of informationsecurity. For the binary series generated by a very long LMAP, if theforemost bits longer than the calculation accuracy is known, throughcalculating the inverse function of the LMAP on the binary bits, x₀ isobtained, and through calculating the LMAP on the x₀, all bits of thevery long binary series can be calculated. But, the upper degree bits(generated earlier) cannot be calculated through the lower degree bits(generated later) of the binary series generated through the LMAP.

If the calculation accuracy is N bits, the number of continuous 0'sgenerated during the calculation of the LMAP is less than N/2. Thefeature limits the possibility of the combination number for the binaryseries generated by the LMAP, but simultaneously ensures that when the Nbits are extracted from the binary series to make a new initial value,the new initial value does not occur the value called a black hole, suchas 0, 0.25, 0.5, 0.75, etc.

When the LMAP is calculated in limited calculation accuracy, the initialvalue sensitivity can be observed in the following forms. Through twoinitial values, in which except for the lowest bit, the other bits inthe two initial values are same, we can ensure that the internal statesx_(t) are in completely different tracks after N times calculation(there is not any relationship between the two internal states), forexample, the results of the initial value 0.0 . . . 01 and 0.0 . . . 010after 128 times calculation in 128 bits calculation accuracy arerespectively 0.0100 . . . 0100 and 0.1100 . . . 0110 (only upper degree4 bits and lower degree 4 bits are shown). There are two meanings.

Firstly, because of the calculation in limited calculation accuracy, thelower degree bits are cast out, thus there is no relationship betweenthe state after N times calculation and the initial state, that is, thestate after N times calculation, not been calculated, cannot beestimated.

Secondly, even if there are two initial values, in which except for thelowest bit, the other bits in the two initial values are same, there isno correlation between the binary series individually generated by thetwo initial values, and the content of one series cannot be estimatedthrough the other series.

The features of the binary series generated through the above LMAP haveimportant implications in the following method for generatingmulti-dimensional random number.

DISCOVERY OF THE INVENTION The Issue Resolved by the Invention

The object of the present invention is to provide a method and devicefor generating and managing random number, which is easily realized ingeneral-purpose computer and special hardware, to generate and manageshorter random number series, such as ID and PW.

The method for generating and managing random number of the presentinvention (claim 1) is for the given N (N is an integer, and N≧2) bitsbinary series R and K dimensions multi-dimensional coordinateinformation i (i1, . . . , ik, . . . , iK) (ik are integer, and ik≧0,k:1, 2, . . . , K), in which R is used for the following part of thedecimal point of initial value x₀ for nonlinear function,x_(t+1)=4x_(t)(1−x_(t)) (herein after referred to as LMAP, 0<x_(t)<1), iis transformed into coordinates of each dimension, i1, . . . , ik, . . ., iK, and x₀ and i1, . . . , ik, . . . , iK are stored in the register;the method with the features including:

-   1) for the initial value x₀ and ik stored in the register, the chaos    computing unit repeatedly implements the calculation of the LMAP in    N bits calculation accuracy through fixed decimal point calculation,    to generate N bits binary series B_(ik), and the bits of B_(ik) are    individually constituted by b_(k·0), b_(k·1), _(. . .) and    b_(k·N−1), wherein b_(k·0)=[2×x_(N×i k)], b_(k·1)=[2×x_(N×i k+1)], .    . . and b_(k·N−1)=[2×x_(N×i k+N−1)], [ ] means the calculation of    casting out the following part of the decimal point;-   2) B_(ik) is then used for the following part of the decimal point    of initial value x₀ through the chaos computing unit repeatedly    implementing the calculation of the LMAP to generate N bits binary    series R_(i1), _(. . .) , _(ik), R_(i1), _(. . .) , _(ik) is R_(i1)    when k=1, . . . , R_(i1), _(. . .) , _(ik) is R_(i1), _(. . .) ,    _(iK) when k=K, and the bits of R_(i1), _(. . .) , _(ik) are    individually constituted by r_(k·0), r_(k·1), _(. . .) and    r_(k·N−1), wherein r_(k·0)=[2×x_(N)], r_(k·1)=[2×x_(N+1)], . . . ,    r_(k·N−1)=[2×x_(2N−1)]; and store the binary series R_(i1), _(. . .)    , _(ik) in the random number register.-   3) the R_(i1), _(. . .) , _(ik) stored in the above random number    register is used for the following part of the decimal point of    initial value x₀ of the LMAP and stored in the above register.

The above operations 1), 2) and 3) are implemented as the order of k=1,2, . . . , K, but R_(i1), _(. . .) , _(iK) do not perform thetransformation of the initial value x₀ of the LMAP when k=K, to generatethe method for generating and managing random number with the feature ofmulti-dimensional random number R_(i).

The device for generating and managing random number of the presentinvention (claim 2) are with the features of the following parts:

-   input unit of generating and managing information for random number,    which receives N (N is an integer, and N≧2) bits binary series R as    the initial value information to generate random number, and K    dimensions multi-dimensional coordinate i (i1, . . . , ik, . . . ,    iK) (ik is an integer, and ik≧0, and K is an integer, and K≧1) as    the multi-dimensional coordinate information;-   initial value/multi-dimensional coordinates transformation unit,    which transforms R, the following part of the decimal point of    initial value x₀ for nonlinear function, x_(t+1)=4x_(t)(1−x_(t))    (herein after referred to as LMAP, 0<x_(t)<1), into x₀, and    transforms I into multi-dimensional coordinates i1, . . . , ik, . .    . , iK to prepare for the calculation of the LMAP to generate random    number;-   register, which stores the initial value x₀ and multi-dimensional    coordinates it i1, . . . , ik, . . . , iK transformed by the initial    value/multi-dimensional coordinates transformation unit;-   chaos computing unit generating chaos binary series, which    repeatedly implements the calculation of the LMAP in N bits    calculation accuracy through fixed decimal point calculation, on the    basis of the initial value x₀ and multi-dimensional coordinates    stored in the register, to generate N bits binary series B_(ik), the    bits of B_(ik) are individually constituted by b_(k·0), b_(k·1),    _(. . .) and b_(k·N−1), wherein b_(k·0)=[2×x_(N×i k)],    b_(k·1)=[2×x_(N×i k+1)], . . . and b_(k·N−1)=[2×x_(N×i k+N−1)], and    [ ] means the calculation of casting out the following part of the    decimal point; and then, B_(ik) is used for the following part of    the decimal point of initial value x₀ and transformed into x₀    through the chaos computing unit repeatedly implementing the    calculation of the LMAP to generate N bits binary series R_(i1),    _(. . .) , _(ik), R_(i1), _(. . .) , _(ik) is R_(i1) when k=1, . . .    , R _(i1), _(. . .) , _(ik) is R_(i1), _(. . .) , _(iK) when k=k,    and the bits of R_(i1), _(. . .) , _(ik) are individually    constituted by r_(k·0), r_(k·1), _(. . .) and r_(k·N−1), wherein    r_(k·0)=[2×x_(N)], r_(k·1)=[2×x_(N+1)], . . . ,    r_(k·N−1)=[2×x_(2N−1)];-   random number register, which stores N bits binary series R_(i1),    _(. . .) ,_(ik) output by the chaos function computing unit; and-   random number generation control unit, which implements the    following operations, including the operation of the input unit of    generating and managing information for random number, the operation    of the initial value/multi-dimensional coordinates transformation    unit, the calculation of the chaos function computing unit, and the    calculation of x₀ transformed from R_(i1), _(. . .) , _(iK), as the    following part of decimal point of the initial value x₀ of the LMAP,    as the order of k=1, 2, . . . , K, but R_(i1), _(. . .) , _(iK) do    not perform the transformation of the initial value x₀ of the LMAP    when k=K, to generate multi-dimensional random number R_(i).

EFFECT OF THE INVENTION

Random number series in the present invention can be quickly generated(regenerated) to be placed at any coordinate position among plenty ofrandom number series in multi-dimensional coordinate space. Therefore,as shown in FIG. 1, we can construct a system for generating andmanaging random number, to generate and manage binary series R_(i) (ID,PW) through managed binary series R and regulated multi-dimensionalcoordinate information i(i1, . . . , ik, . . . , iK).

Because of the chaos function (LMAP) used in the present invention,there is no linear relationship between the R_(i) generated by regulatedmulti-dimensional coordinate information i (i1, . . . , ik, . . . , iK).Thus, R cannot be estimated through certain random number series R_(i)and multi-dimensional coordinate information i (i1, . . . , ik, . . . ,iK) thereof. Also, the random number series generated by othermulti-dimensional coordinate information cannot be estimated.

Still because of the LMAP calculated through fixed decimal pointcalculation in the present invention, the system for generating andmanaging random number proposed by the present invention is easilyconstructed by a system implementing integer arithmetic, (such asmultiplication, addition, subtraction, and logical operations) whetherit is a software or hardware system. Furthermore, the present inventionmakes the low price of the system for generating and managing randomnumber possible to be an expected form in industrial technology.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a system for generating and managingrandom number according to the present invention;

FIG. 2 is a composition diagram showing the implementation form of adevice for generating random number according to the present invention;

FIG. 3 shows the method for generating one-dimensional random number;

FIG. 4 shows the method for generating two-dimensional random number;

FIG. 5 is a flowchart showing the embodiment of the action of the devicefor generating and managing random number 100;

FIG. 6 is a table showing the product numbers of industrial productstransformed into multi-dimensional coordinates; and

FIG. 7 is a table showing the time needed for the random numbergenerated by the method for generating multi-dimensional random number.

DETAILED DESCRIPTION OF THE INVENTION

Hereinafter, the embodiments and the effects of the present inventionwill be described with reference to the drawings.

FIG. 2 shows an embodiment of the present invention, which is the devicefor generating and managing random number 100. The device for generatingand managing random number 100 in the embodiment generates N bits binaryseries R_(i1), _(. . .) , _(ik) by way of chaos computing unit, throughtransforming N bits binary series R into initial value x₀ of the LMAP,and on the basis of x₀ and multi-dimensional coordinate information i,and then the calculation of transforming R_(i1), _(. . .) , _(ik) intox₀ is repeatedly implemented for K times, to generate K-dimensionalrandom number R_(i). The device for generating and managing randomnumber 100 is instituted by input unit of generating and managinginformation for random number 102, initial value/multi-dimensionalcoordinates transformation unit 104, register 106, chaos functioncomputing unit 108, random number register 110, and random numbergeneration control unit 112.

The input unit of generating and managing information for random number102 receives N bits binary series R and multi-dimensional coordinateinformation I (i1, . . . , iK).

The initial value/multi-dimensional coordinates transformation unit 104transforms the input binary series R or the binary series R_(i1),_(. . .) , _(ik) generated during the generation of themulti-dimensional random number into x₀, and transforms the inputmulti-dimensional coordinate information i into each dimensioncoordinates i1, . . . , iK for fixed decimal point calculation togenerate multi-dimensional random number.

The register 106 stores x₀ and i1, . . . , iK transformed in the initialvalue/multi-dimensional coordinates transformation unit 104.

The initial value stored in the register 106 is used by the chaosfunction computing unit 108 as the order of multi-dimensional coordinateik (k=1, 2, . . . , K) to repeatedly calculate the LMAP, to generate Nbits binary series R_(i1), _(. . .) , _(ik).

The detailed operations of the chaos function computing unit aredescribed as following.

Firstly, the initial value x₀ and multi-dimensional coordinate ik storedin the register 106 are used by the chaos function computing unit 108 tocalculate the LMAP for N×ik times.

Next, while in the calculation of the LMAP, b_(k·0)=[2×x_(N×i k)],b_(k·1)=[2×x_(N×i k+1)], . . . and b_(k·N−1)=[2×x_(N×i k+N−1)] arecalculated, in which [ ] means the calculation of casting out thefollowing part of the decimal point, to generate N bits binary seriesB_(ik)(b_(k·0), b_(k·1), _(. . .) , b_(k·N−1)).

Then, B_(ik) is used for the following part of the decimal point ofinitial value x₀ of the LMAP, to calculate the LMAP for N times.

And then, while in the calculation of the LMAP, r_(k·0)=[2×x_(N)],r_(k·1)=[2×x_(N+1)], . . . and r_(k·N−1)=[2×x_(2N−1)] are calculated, togenerate N bits binary series R_(i1,) _(. . .) , _(ik)(r_(k·0), r_(k·1),. . . , r_(k·N−1)).

Because of the above additional calculation, we can cut off theabove-mentioned possibility of speculating the lower degree bits fromthe upper degree bits in the binary series generated through the LMAP.

The random number register 110 is used for storing the binary seriesoutput by the chaos function computing unit 108.

The random number generation control unit 112 controls the operations ofevery unit to generate multi-dimensional random number series.

The random number generation control unit 112 repeatedly calculates onthe basis of K dimensions multi-dimensional information as the order ofk=1 to k=K, through the chaos function computing unit, and the outputsare stored in the random number register 110; if k<K, the random numberseries stored in the random number register 110 is transformed into x₀through the initial value/multi-dimensional coordinates transformationunit 104, and the x₀ is stored in the register 106, and the calculationis gone on; if k=K, the N bits binary series stored in the random numberregister 110 is used for the random number R_(i), and the calculation isterminated.

The meaning and effect of the multi-dimensional random number aredescribed as following.

We consider the fixed decimal point calculation to the LMAP with N bitscalculation accuracy to generate N bits binary series.

N bits initial value x₀ is input to generate the required number ofbinary series r (r₀, r₁, . . . ). We assume that the generation speed ofthe random number generator is S bps (bits/sec), and the operationaltime, except for generating binary series, is too short, so not becounted. Here we take a look at that, if the random number generatorgenerates M×N (M is an integer, and M≧1) bits random number, therequired time for generating any one of R_(i) through initial value x₀,when the random number is divided into M series and each one is N bitsbinary series.

The series R_(i) generated through this way can be imagined to be put ona straight line (as shown in FIG. 3), thus, the generation method isreferred to a method for generating one dimension random number series.

It is clear that, because of N bits series, the required time forgenerating the first series R₀ through x₀ is N/S. The required time forgenerating the second series R₁ through x₀ is 2N/S because it includesthe time for generating the first random number series. Thus, therequired time for generating the ith series R_(i−1) through x₀ is i×N/S.

Because the more generated random number series, the better, a greater Mis expected. But, as for such method for continuously generating randomnumber series through one initial value, M cannot be very large, such asM=2⁶⁴, even if the generation speed is 2⁴⁰ bps, the average generatingtime for N bits series is (1+2⁶⁴)×N/2⁴⁰>2²⁴ seconds.

We will consider the following method for generating random number.Here, we assume the M is M₁×M₂ (M₁, M₂ are integers, and M₁, M₂≧1), M₁series N bits random number series are generated through N bits initialvalue x₀, the generated M₁ series N bits random number series are usedfor new initial values, to individually generating M₂ series N bitsrandom number series. The generated N bits random number series arerepresented as R_(i1·i2) (i1=0, . . . , M₁−1, i2=0, . . . , M₂−1).

The series R_(i1),_(i2) generated through the above way can be imaginedto be put on a two-dimensional plane (coordinates), thus, the generationmethod is referred to a method for generating two-dimensional randomnumber series.

It is clear that the total number of R_(i1), _(i2) is M₁×M₂=M, therequired time T for generating any one R_(i1), _(i2) through initialvalue x₀ is as following.T _(R) _(0,0) =(1×N+1×N)/S=2N/ST _(R) _(0,1) =(1×N+2×N)/S=3N/ST _(R) _(0,i2) =(1×N+(i2+1)×N)/S=(i2+2)N/ST _(R) _(i1,i2) =((1+i1)×N+(i2+1)×N)/S=(i1+i2+2)N/S

That is, as for the required time for generating one random numberseries, the minimum is 2N/S, and the maximum is (M₁+M₂)N/S, comparedwith the longest time, M×N/S=(M₁×M₂)N/S, for the method for generatingone dimension random number series, the difference is self-evident.

We assume that K dimensions and M=M₁× . . . ×M_(K), M₁ series N bitsrandom number series are generated through N bits initial value x₀.Then, the generated M₁ series N bits series are used for new initialvalues, to individually generate M₂ series N bits random number series.Till M_(K), the transformations for new initial values are performed forK−1 times to generate series R_(i). The series R_(i) can be imagined tobe coordinates (i: i1, i2, . . . , iK) put in K dimensions space, thus,the generation method is referred to a method for generating Kdimensions random number series. We can understand that, the requiredtime for any one series in K dimensions coordinate space is (K+i1+i2+ .. . +iK)N/S, the minimum is KN/S, the maximum is (M₁+M₂+ . . . +M_(K))N/S, and the average time is (K+M₁+M₂+ . . . +M_(K))N/(2S).

The meanings of every parameter N, K(k), M(Mk) in the method forgenerating multi-dimensional random number are described as following.

N is calculation accuracy. Therefore, the variety of initial value(initial value space) available is 2^(N)−4, except for 0 . . . 0, 010 .. . 0, 10 . . . 0, 110 . . . 0 (0, 0.25, 0.5, 0.75). But, because thelength of chaos state generated through certain initial value x₀ issimilar to 2^(N/2), we can estimate the value of non-periodic M is2^(N/2)/N. Actually, when N is assumed to be a value between 32 and 64,the search result through numerical calculation to the length ofnon-periodic M is similar to 2^(N/2). This is because the generation ofthe initial values through repeatedly calculation makes the periodicityof multi-dimensional random number generator to be longer than that ofthe original LMAP.

The coordinate volume M is the total of the series generated throughinitial value x₀. The value is generally restricted by the periodicityof random number generator. However, if same random number series isallowed being placed in multi-dimensional space (an unspecificlocation), there is no such restriction.

The space of every dimension coordinate depends on M_(k) (k=1, 2, . . ., K). Also, the generation speed of R_(i) depends on M_(k). When M_(k)is assumed to be larger, the average generation speed of R_(i) would bemuch slower. M_(k) and k together have the classification function toR_(i). Namely, the information with specific meanings (such as time,name, organization (department), etc.) can be possessed. That is, whenthe decision for the appropriate value of M_(k) is made, not onlygeneration speed of random number, but also classification ease, must bethought over. The more effective representing way for coordinate spaceis assumed M=2^(m), m=m₁+ . . . +m_(K)(m₁, . . . , m_(K) are integers,and m₁, . . . , m_(K)≧0).

K is used for dimension number, possessing classification function. WhenM is constant, if K is larger, the average value of M_(k) will besmaller, and the average generation speed of R_(i) will be faster.However, if the individual M_(k) is extremely larger, generation speedof R_(i) may be extremely slower. This is because, like the method forgenerating one dimension random number series, if the coordinate numberin certain dimension is assumed too large, the average generation timein this dimension will be very long. Therefore, the setting of K is notonly following the classification function, but also making individualM_(k) not too large. That is, even of the same classification, there isno need to represent as the same dimension coordinate. In theclassification, when the individual M_(k) is too large, it can berepresented as plural dimensions.

K(k) can be divided.

We will think about a multi-dimensional random number generation system,including N bits calculation accuracy, initial value x₀, and Kdimensions, and the magnitude of every dimension is M₁, M₂, . . . ,M_(K). We inspect the state of k dimension in the intermediate process.

When k=1, M₁ N bits binary series R_(i1) are generated through initialvalue x₀. When k=2, M₁ N bits binary series R_(i1) (initial value in theintermediate process) are generated through initial value x₀, then, M₂ Nbits binary series R_(i1),_(i2) are individually generated throughinitial value in the intermediate process. Namely, total M₁×M₂ N bitsbinary series can be generated through initial value x₀. Also, the kdimension in intermediate process can generate M₁×M₂× . . . ×M_(k)initial values in intermediate process.

Here, we assume k=Ku and K=Ku+Kd, then Kd=K−Ku. That is, which is themulti-dimensional random number generation system constituted by theupper degree dimension of initial value x₀ with Ku dimensions and thevalues of every dimension are M₁, M₂, . . . , M_(ku). For example,M₁×M₂× . . . ×M_(ku) N bits binary series (the initial value inintermediate process) generated through the system constituted by theupper degree dimension of Ku dimensions are used for themulti-dimensional random number generation system (Kd dimensions and thevalues of every dimension are M_(ku+1), M_(ku+1), . . . , M_(K)) ofevery initial value, which is constituted by the lower degree dimension.

As mentioned above, two K's (Ku, Kd) correspond to a multi-dimensionalrandom number generation system, through dividing K, themulti-dimensional random number occurs system-division, and when themulti-dimensional random number generation system is divided, through Kudimension as the margin, not all lower degree dimensions should bedivided from the multi-dimensional random number generation system. Onlythe random number R_(i1),_(i2),_(. . . , iku) at the arbitrarycoordinates i1, i2, . . . , i(ku) in intermediate process are output tobe the initial value of the new lower degree multi-dimensional randomnumber generation system, arbitrary lower degree multi-dimensionalrandom number generation system can be divided from the originalmulti-dimensional random number generation system.

Furthermore, it is clear that the inverse operation of thesystem-division should connect (integrate) with the divided system.However, the individual coordinate information in intermediate processdimension during division should be kept. In other words, theintermediate dimensional coordinate information of the divided systemwith the need of re-connection should be kept. The intermediate processcoordinate of completely independent divided system without the need ofre-connection may be removed.

The above describes the division for K into Ku and kd, and, of course,more division can be performed as needed through same method.

The value of R_(i) generated from multi-dimensional coordinates i (i1,i2, . . . , iK) through initial value x₀ and that of R, generated frommulti-dimensional coordinates i (i (ku+1), i (ku+2), . . . , iK) throughinitial value R_(i1), _(i2), _(. . . , iku) are same. That is, initialvalue R_(i1), _(i2), _(. . . , iku) can be obtained from initial valuex₀, but initial value x₀ cannot be obtained from R_(i1), _(i2),_(. . . , iku). As for the above initial value with such relationship,initial value x₀ is referred to upper degree initial value, and R_(i1),_(i2), _(. . . , iku) is referred to lower degree initial value.

By way of the multi-dimensional random number generation method with theabove features, we can construct random number generation system withgrade structure. That is, the competence of the upper degree initialvalue x₀ and that of the lower degree initial value R_(i1), _(i2),_(. . . , iku) are different, the keeper of initial value x_(o) hasgreater competence than that of R_(i1), _(i2), _(. . . , iku).

FIG. 5 is a flowchart showing an embodiment of the action of the devicefor generating and managing random number 100. The device for generatingand managing random number 100 shown in the flowchart starts actionaccording to the order generated by the random number.

The input unit of generating and managing information for random number102 receives the input N bits binary series R and multi-dimensionalcoordinate information i, and variable k is assumed as k=0. Then, theinitial value multi-dimensional coordinates transformation unit 104makes k=k+1, and transforms the received N bits binary series R into x₀(S104) and stores x₀ and multi-dimensional coordinate information (i1,i2, . . . , iK) into the register 106 (S106). According to x₀ andmulti-dimensional coordinate information ik stored in the register 106,the chaos function computing unit 108 further generates N bits binaryseries R_(i1), _(i2), _(. . . , ik), and stores them into the randomnumber register 110 (S108); when k<K (dimension number), N bits binaryseries R_(i1), _(i2), _(. . . , ik) are input the initialvalue/multi-dimensional coordinates transformation unit 104 (S110), andre-calculation is performed from (S104). When k=K, N bits binary seriesR_(i1), _(i2), _(. . . , ik) are output as random number (S112), and theoperation of the device for generating and managing random number 100 inthe flowchart terminates.

Here, by way of the embodiment of the system for generating and managingrandom number, the effect of the present invention is confirmed throughinitial value sensitivity, irrelevancy of adjacent coordinates,generation speed, and system-division.

Industrial products include the identification of the product mark(number). For example, model number, manufacture number, batch number,manufacture date, etc, these numbers are necessary for managing relatedinformation of the product and after-sales service. Of course, thesenumbers must be managed. Most of the numbers of products are regularconsecutive numbers. Because of regularity, the message content in thesenumbers is less and easy to be managed. However, on the other hand, itis easy to infer other numbers from a number and to be illegally used,such counterfeit attached with authentic number to pose as genuinearticle. If the regular number is integrated with irregularidentification ID number (random number), the product number cannot beinferred. However, using the irregular random number will make itdifficult to manage near-infinite numbers of industrial products. Themulti-dimensional random number generation method proposed in thepresent invention is effective to manage the irregular identification ID(random number series).

We assume three elements (R, i, R_(i)) corresponding tomulti-dimensional random number generation method, which transform(unique) product number identifying product into multi-dimensionalcoordinate, and integrate the generated product identification ID(random number R_(i)) with the product number to make it non-inferable.At this point, initial value x₀(R) becomes the management key formanaging product identification ID. The correct initial value x₀ andproduct number can generate (regenerate) corresponded productidentification ID. The regular product number can be inferred, but theattached product identification ID cannot be. That is, without initialvalue x₀, it is impossible to obtain correct combination of productnumber and product identification ID.

The following is an example of simplified generation for identificationID of the product with model number MC780 and manufacture numberC042875.

The generation for identification ID needs to transform the productnumber into multi-dimensional coordinate. As shown in FIG. 6, thetransformation for model number and manufacture number is performed.(The English letters are represented as hexadecimal in ASCII code, anddecimal digits are represented as hexadecimal.)

We assume dimension number K=14, the values of every dimension areM₁=M₂= . . . =M₁₄=16, and management key is 128 bits initial value x₀=0_(. . .) 01 (hexadecimal), thus, R_(i) calculated throughmulti-dimensional random number generation method is represented inhexadecimal as B44768B06B7A25D464F3523552BD0DFB. The correspondedmulti-dimensional coordinate is represented in hexadecimal as(i=4,D,4,3,2,C,4,4,3,0,A,7,7,B).

Firstly, multi-dimensional coordinate i is fixed, and x₀ is given minorchanges, to identify the generated changes of R_(i). The following showsthe embodiment when multi-dimensional coordinate i is(4,D,4,3,2,C,4,4,3,0,A,7,7,B). When x₀ is 0 . . . 01 and 0 . . . 02 (32digits in hexadecimal), R_(i) is (B44768B06B7A25D464F3523552BD0DFB) and(8849A5994E6b861F6298CFB4C7C71E9F), respectively. We can confirm theinitial value sensitivity.

Then, initial value is fixed, and multi-dimensional coordinate i isgiven minor changes, to identify the generated changes of R_(i). Thefollowing shows the embodiment when initial value x₀ is 0 . . . 01. Whenmulti-dimensional coordinate i is (4,D,4,3,2,C,4,4,3,0,A,7,7,B) and(4,D,4,3,2,C,4,4,3,0,A,7,7,C), R is (B44768B06B7A25D464F3523552BD0DFB)and (BA1359675D951215D6F14411426D1E13), respectively. We can confirm theirrelevancy of adjacent coordinates.

From the above results, we can confirm the following effects; as for therandom number generator constructed through multi-dimensional randomnumber generation method, even if the system configuration is same,there is no relationship between the random numbers generated throughdifferent initial values and same multi-dimensional coordinate. That is,even the system are constructed the same, it is impossible to infer theinitial value from the random number of the same multi-dimensionalcoordinate. Also, from the random number series at certainmulti-dimensional coordinate, it is impossible to infer the randomnumber series at the adjacent multi-dimensional coordinate.

As shown in the above, when the generation speed of binary series isgiven, the required time for generating the random number series atcertain multi-dimensional coordinate is obtained. At this point, weassume that the operation time, except for generating binary series, istoo short, so not be counted. Here, the generation time calculatedthrough approximation is inferred time t, the actual required time forgeneration is example time t′, and when the generation speed of binaryseries is 4.9 Mbps, the results of the both are shown as in FIG. 7. Wecan confirm which are close and the generation speed can be practicallyapplied.

In the system for generating product identification ID, the productnumber is instituted by model number and manufacture number, that is,the product number is divided into a portion for managing model (modelnumber) and a portion for managing the product of the model (manufacturenumber). Here, the product number is divided into model number andmanufacture number, to confirm the random numbers respectively generatedin divided and undivided situations.

When initial value x₀ is 0 . . . 01 and multi-dimensional coordinate iis (4,D,4,3,2,C,4,4,3,0,A,7,7,B), the random number series R_(i) isgenerated as shown in the above. Firstly, the multi-dimensionalcoordinate is divided into (4,D,4,3,2,C,4) (model management) and(4,3,0,A,7,7,B) (the product of the model). Then, the random numberseries R_(i′) is generated through initial value x₀ (0 . . . 01) andmulti-dimensional coordinate i′ (4,D,4,3,2,C,4). And then, the randomnumber series R_(i″) is generated through the initial value transformedfrom R_(i′) and multi-dimensional coordinate i″ (4,3,0,A,7,7,B), andcompared with the random number series R_(i) when undivided. We canconfirm the results are the same.

The required times for individually generating R_(i′) and R_(i″) throughdivided multi-dimensional coordinate are 0.001437 seconds and 0.001421seconds, respectively, and the sum of those is close to the time0.002781 seconds when undivided.

As mentioned above, even only the initial value and themulti-dimensional coordinate are changed, without changing calculationmethod, the subsystem is easily separated from the parent system. Thecalculated quantity is reduced after division, and the generation speedof the random number is faster.

In addition, because of division, it is not necessary for the lowerdegree system keeping the information of the upper degree system, thus,the upper degree system becomes safer from the viewpoint of informationsafety. Such as the situation of the product management system, whenproduction department of certain product migrates abroad, the divisionof the management system is effective.

According to the present invention, the proposed method for generatingand managing random number can generate and manage irregular M series Nbits binary series R_(i) through one series N bits binary series R(initial value) and regular M multi-dimensional coordinate information i(FIG. 1).

According to the present invention, the random number generation isperformed through R and regular i to generate R_(i), in which it ischaracterized that it is impossible to infer another features of R_(i)or R through one given i or R_(i). The random number generator with suchfeatures can be applied to a wide range of areas of informationsecurity.

One-time system for identification of ID and PW can be constructedthrough random number generation method of the present invention. Thatis, the secret (ID and PW) kept at system side and user side is used forR, R and new i are used for generating R_(i) (for identification of IDand PW) at user side, and i and R_(i) are delivered to system side forevery identification. At system side, the received i and R of the userare used for generating R_(i) compared with the delivered R_(i) foridentification. Because of one-time i, even if it is tapped, there wouldnot be any problem. Also because of secret R without being delivered(through communication network), it is further safer. If R is made ofinformation adopted from human body, such as fingerprint, vein, etc, itis not necessary to memorize R.

If the random number generation method of the present invention isapplied to system for generating and managing key in encryption system,the so-called strongest encryption method is realized, that is, theencryption method with one-time key. Because multi-dimensionalcoordinate information i is only used once, it is impossible to use samekey again.

If the random number generation method of the present invention isapplied to common key encrypted communication, between two sides keepingsame keys R, the information is encrypted by one-time key R_(i). Onlyencrypted information and i are delivered, and it is not necessary todeliver R. The other side receiving the encrypted information and i useskept R and i for generating R_(i) to recover the information. Because Ris not shown in communication, it is further safer.

Because the random number generation of the present invention calculatesEquation 1 through fixed decimal point calculation, the calculation canbe performed through integer operations. Also because integers caneasily perform division calculation, even different calculation system,such as general-purpose computer (various OS), dedicated hardware,microcomputer, etc, only basic integer arithmetic implemented, forexample, addition, multiplication, bit shift, logical operation betweenbits, etc, same output is obtained through same input.

Therefore, the random number generation device of the present inventionhas various combinations adapted for “performance-cost” needed, ishighly scalable, and can be applied to a wide range of industriescentered on information security areas.

As shown in the above, the present invention is described throughembodiments, however, the technical means are not limited in the rangeof these embodiments. These embodiments can be modified or improved asneeded. The present invention generates binary series through Equation1, but the other methods generating binary series are available.Moreover, these embodiments can be modified on the basis of generationefficiency and features of random number. It is clear that, as for suchmodification, the improved patterns are included within the range of thetechnology of the present invention.

What is claimed is:
 1. A method for generating and managing random numbers, comprising steps of: an input circuit setting a binary series R with binary integer having N bits (N≧2 and N is an integer) and multi-dimensional coordinate information i for K dimensions (i1, . . . , ik, . . . , iK) (ik is an integer, and ik ≧0, k:1, 2, . . . , K), wherein R is a decimal portion of an initial value x₀ for a nonlinear function, x_(t+1)=4 x_(t)(1−x_(t)) (hereinafter referred to as LMAP, 0<x_(t)<1, t=0,1,2, . . . ), and said coordinate information i is then transformed into coordinate value of each dimension (i1, . . . , ik, . . . , iK) by a transforming circuit; and x₀, i1, . . . , ik, . . . , iK are stored in a register; 1) according to the initial value x₀ and ik, an LMAP circuit implementing LMAP calculation having the accuracy of N bits through a fixed decimal point calculation, which is repeatedly done by chaos computing to generate N bits binary series B_(ik), and bits of B_(ik) are individually constituted by b_(k·0) b_(k·1) . . . b_(k·N−1), wherein b_(k·0)=[2×x_(N×i k)], b_(k ·1)=[2×x_(N×i k+1)], . . . and b_(k·N−1)=[2×x_(N×i k+N−1)], and [ ] represents a calculation of removing decimal portion; 2) a chaos computing circuit implementing the chaos computing on B_(ik) as a decimal portion of the initial value x₀ after LMAP and repeatedly conducting calculation of the LMAP to generate and store an N bits binary series R_(i 1), _(. . .) , _(i k)(when k=1, R_(i 1), _(. . .) , _(i k) is R_(i 1), _(. . .) , _(i K); and when k=K, R_(i 1), _(. . .) , _(i k) is R_(i 1), _(. . .) , _(i K), wherein the bits of R_(i 1), _(. . .) , _(i k) are individually constituted by r_(k·0), r_(k·1), . . . and r_(k·N−1), and r_(k·0)=[2×x_(N)], r_(k·1)=[2×x_(N+1)], . . . , r_(k·N−1)=[2×x_(2N−1)], which are stored in a random number register; 3) using said R_(i 1), _(. . .) , _(i k) stored in the random number register as a decimal portion of initial value x₀ of the LMAP and storing it to said register; and a random number generation control circuit implementing the above operations 1), 2) and 3) as the order of k=1,2, . . . , K, but when k=K, operation 3) is stopped, and operation 2) is used to generate R_(i 1), _(. . .) , _(i K) as random numbers.
 2. A device for generating and managing random numbers, including: an input circuit of generating and managing information for random number, which receives N (N is an integer , and N≧2) bits binary series R as an initial value information to generate random number, and multi-dimensional coordinates i for K dimensions (i1, . . . , ik, . . . , iK) (ik is an integer, and ik≧0;K is an integer, and K≧1)having multi-dimensional coordinate information; an initial value/multi-dimensional coordinates transformation circuit, which transforms R, decimal portion of initial value x₀ for nonlinear function, x_(t+1)=4x_(t)(1−x_(t)) (herein after referred to as LMAP, 0<x_(t)<1), into x₀, and transforms i into multi-dimensional coordinates i1, . . . , ik, . . . , iK for the LMAP to generate random number; a memory, which stores the initial value x₀ and multi-dimensional coordinates i1, . . . , ik, . . . , iK transformed by the initial value/multi-dimensional coordinates transformation circuit; a chaos computing circuit generating chaos binary series, which repeatedly implements calculation of the LMAP in N bits calculation through a fixed decimal point calculation, on the basis of the initial value x₀ and multi-dimensional coordinates stored in the register, to generate N bits binary series B_(ik), bits of B_(ik) are individually constituted by b_(k·0) b_(k·1) . . . b_(k·N−1), wherein b_(k·0)=[2×x_(N×i k)], b_(k·1)=[2×x_(N×i k+1)], . . . and b_(k·N−1)=[2×x_(N×i k+N−1)], and [ ] represents an operator used to remove decimal portion, and B_(ik) is used for the decimal portion of initial value x₀ and transformed into x₀ through the chaos computing circuit repeatedly implementing the calculation of the LMAP to generate N bits binary series R_(i 1), _(. . .) , _(i k), R_(i1), _(. . .) , _(ik) is R_(i1) when k=1, . . . , R_(i 1), _(. . .) , _(i k) is R_(i 1), _(. . .) , _(i K) when k=K, and the bits of R_(i 1), _(. . .) , _(i k) are individually constituted by r_(k·0), r_(k·1), . . . and r_(k·N−1), wherein r_(k·0)=[2×x_(N)], r_(k·1)=[2×x_(N+1)], . . . , r_(k·N−1)=[2×x_(2N−1)]; a random number memory, which stores N bits binary series R_(i 1), _(. . .) , _(i k) output by the chaos computing circuit; and a random number generation control circuit, which implements following operations, including an operation of the input circuit of generating and managing information for random number, an operation of the initial value/multi-dimensional coordinates transformation circuit, a calculation of the chaos computing circuit, and a calculation of x₀ transformed from R_(i 1), _(. . .) , _(i K), as the decimal portion of the initial value x₀ of the LMAP, as the order of k=1,2, . . . , K, but R_(i 1), _(. . .) , _(i K) do not perform the transformation of the initial value x₀ of the LMAP when k=K, to generate multi-dimensional random number R_(i). 